As the West sank into recession in 2008, Chinese tycoon Chen Feng decided it was time to stretch his wings.

Mr. Chen’s conglomerate, HNA Group, already had a collection of domestic assets that spanned hotel chains, supermarkets, shipping firms and Hainan Airlines, the country’s biggest privately held airline. The next place to go, Mr. Chen told a local business magazine, was overseas, where the financial crisis was making assets...